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Mathematics
Differential Equations
Deriving the FEA formulation using triangular elements
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[QUOTE="bigfooted, post: 6160435, member: 377103"] Here's a book that is low on math and high on worked out examples that you can follow by hand: [URL]https://www.amazon.com/dp/0070087148/?tag=pfamazon01-20[/URL] You might also want to study this in case you haven't done so already: [URL]https://www.amazon.com/dp/0070552215/?tag=pfamazon01-20[/URL] You probably know chapters 1 and 2, study chapters 3 and 6 for 2D stuff. If you want to know why it works, you have to know about the variational form though. The first thing to learn is how to transform any triangle and rectangle to the unit triangle or rectangle. Then learn how to integrate a function on any triangle by transforming it to the unit triangle. Then realize that solving the pde in variational form just means discretizing the domain into a lot of triangles, transforming the problem from the unit triangle (because all these neat integration methods only work from -1..+1) to the actual triangle, and construct the global mass matrix and solve the system Ax=b It helps to write an actual solver in e.g. matlab, scilab, python or whatever you have available that has some basic matrix-vector stuff. 1. no, the integral is in 2D. The number of nodes does increase the size of the matrix. Try to see this by just integrating a function in 2D on some rectangle (with known solution so you can check the outcome). 2. After discretization, the integration becomes the sum of the integration over the unit triangle/rectangle. Hope this helps. [/QUOTE]
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Deriving the FEA formulation using triangular elements
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